Dr. Post-Training: A Data Regularization Perspective on LLM Post-Training

Abstract

Data selection methods address a critical challenge in LLM post-training: effectively leveraging scarce, high-fidelity target data alongside abundant but imperfectly aligned general training data. In this work, we move beyond the data-selection framing and introduce Dr. Post-Training (Data-Regularized Post-Training), a novel framework that reconceptualizes general training data as a data-induced regularizer that prevents overfitting to the scarce target objective, rather than serving as a pool for selection. Specifically, our framework proposes that, at each training step, we construct a feasible set of model update directions using the general training data, and project the model update direction specified by the scarce target data onto that feasible set. Standard training and existing data selection methods arise as special cases with different choices of the data-induced regularizer, and these methods correspond to different points on a bias-variance spectrum with different regularization strengths. Building on this view, we propose a family of methods offering a richer design space and more flexible bias-variance tradeoffs. For practical LLM-scale use, we introduce careful system optimizations that realize these methods with minimal overhead. Extensive experiments across SFT, RLHF, and RLVR show that our methods outperform standard training and state-of-the-art data selection baselines, with the largest gains where the general and target data are most misaligned, and system benchmarks confirm their efficiency.